Tesla Motors Inc. plans to offer hands-free highway driving in its Model S electric sedans in 2015, putting it as much as a year ahead of other luxury brands in offering autopilot functions in automobiles, according to people familiar with the company’s plans.

Other auto makers, including General Motors Co. and Volkswagen AG’s Audi, have said they’re aiming to launch hands-free highway driving systems by roughly 2016. Daimler AG’s Mercedes-Benz now sells a system that can pilot a car on a freeway, but it is designed so that...